Tanzania, August, 2019
# insert fancy example leaflet map with several components 1 + 1
## [1] 2
leaflet() initialises a leaflet object m. Pipe this into addCircles() where we refer to the map_data dataframe and indicate which columns correspond to latitude and longitude.
m <- leaflet() %>% addCircles(data = map_data, lng = ~x, lat = ~y) m
Tile give our data geographic context. addTiles() uses OpenStreetMap tiles, the default for leaflet
m %>% addTiles()
addProviderTiles()Allows us to use third party tiles (e.g. Terrain tiles from Stamen Design).
# m created using code from previous slides m <- leaflet() %>% addCircles(data=map_data, lng=~x, lat=~y)
Code options
addProviderTiles(map = m, provider = "Stamen.Terrain") addProviderTiles(map = m, provider = providers$Stamen.Terrain) m %>% addProviderTiles(provider = providers$Stamen.Terrain)
addProviderTiles()m %>% addProviderTiles(providers$Stamen.Terrain)
Try some options for provider tiles.
Hint: Use tab completion with addProviderTiles(provideer = providers$) to access options
addProviderTiles()m %>% addProviderTiles(providers$Esri.NatGeoWorldMap)
addProviderTiles()m %>% addProviderTiles(providers$Wikimedia)
addProviderTiles()m %>% addProviderTiles(providers$Esri.WorldTopoMap)
addProviderTiles()m %>% addProviderTiles(providers$Esri.WorldImagery)
addProviderTiles()m %>% addProviderTiles(providers$CartoDB.Positron)
addProviderTiles()https://github.com/leaflet-extras/leaflet-providers
Full list of free-to-use tiles with previews:
http://leaflet-extras.github.io/leaflet-providers/preview/index.html
Tile servers based on OpenStreetMap data with info on how to cite:
https://wiki.openstreetmap.org/wiki/Tile_servers
e.g. When using the tiles provider$CartoDB.Positron:
Figure 1. Map of Tanzanian dataset. Cases coloured blue. Map tiles by Carto, under CC BY 3.0. Data by OpenStreetMap, under ODbL.
An interactive way for the user to get more info on data points
Easier to first store what we want to display as an object popupInfo
popupInfo <- paste("Date: ", map_data$date, "<br>",
"Species: ", map_data$species, "<br>",
"Age: ", map_data$age, "<br>",
sep = " ")
m <- leaflet() %>% addProviderTiles(providers$CartoDB.Positron)
Then, refer to popupInfo when using addCircles(), addCircleMarkers() etc.
m %>% addCircles(data = map_data, lng = ~x, lat = ~y, popup = popupInfo)
An interactive way for the user to get more info on data points
m %>% addCircles(data = map_data, lng = ~x, lat = ~y, popup = popupInfo)
Labels show up when hovered over, popups when the user clicks.
m %>% addCircles(data = map_data, lng = ~x, lat = ~y, popup = popupInfo,
label = ~species)
Circle markers (addCircleMarkers()) are similar to circles but radius in onscreen pixels is constant regardless of zoom level.
m %>% addCircleMarkers(data=map_data, lng=~x, lat=~y, popup = popupInfo, radius = 5,
stroke = T, weight = 3, color = "grey", opacity = 0.8,
fillColor = ifelse(map_data$species == "human",
"firebrick", "dodgerblue"), fillOpacity = 0.7)
With, stroke = F, weight, color, and opacity are irrelevant. Can also use radius = to size circle markers by species.
m %>% addCircleMarkers(data = map_data, lng = ~x, lat = ~y, popup = popupInfo, stroke = F,
radius = ifelse(map_data$species == "human", 8, 4),
fillColor = ifelse(map_data$species == "human", "firebrick", "dodgerblue"),
fillOpacity = 0.8)
On a map with many markers, it might make sense to cluster them using clusterOptions = markerClusterOptions() shown here with the default options for markerClusterOptions().
m %>% addMarkers(data = map_data, lng = ~x, lat = ~y, label = ~species, popup = popupInfo)
On a map with many markers, it might make sense to cluster them using clusterOptions = markerClusterOptions() shown here with the default options for markerClusterOptions().
m %>% addMarkers(data = map_data, lng = ~x, lat = ~y, label = ~species, popup = popupInfo,
clusterOptions = markerClusterOptions())
colorFactor()leaflet::colourFactor() creates a function (we're going to call it myPal) that is used as an argument when we use addCircles(), addCircleMarkers()etc.
# Choose 3 colours for our 3 groups
colour_pal <- c("gold", "forestgreen", "cornflowerblue")
myPal <- colorFactor(palette = colour_pal,
domain = c("Human", "Domestic", "Wildlife"))
Create a fresh version of m before we add coloured circles
m <- leaflet() %>% addProviderTiles(provider = providers$CartoDB.Positron)
colorFactor()myPal() takes species type variable as argument
m <- m %>% addCircles(data=map_data, lng=~x, lat=~y,
color = myPal(map_data$species_type),
opacity = 0.9, popup = popupInfo)
m
m <- m %>% addLegend(position = "topright", title = "Species<br>type", pal = myPal,
values = map_data$species_type, opacity = 0.9)
m
Adapt the code from previous slides to produce a map with:
1) tiles showing topography
2) circles coloured by species (instead of species type)
3) a colour legend
4) a scale bar showing distance in kilometers (hint: ?addScaleBar).
Previous code:
colour_pal <- c("gold", "forestgreen", "cornflowerblue")
myPal <- colorFactor(colour_pal, domain = c("Human", "Domestic", "Wildlife"))
m <- leaflet() %>%
addProviderTiles(provider = providers$CartoDB.Positron) %>%
addCircles(data = map_data, lng = ~x, lat = ~y,
color = myPal(map_data$species_type), opacity = 0.9) %>%
addLegend(position = "topright", title = "Species<br>type", pal = myPal,
values = map_data$species_type, opacity = 0.9)
m
Part 1) tiles showing topography
m <- leaflet() %>% addProviderTiles(provider = providers$OpenTopoMap) m
Part 2) circles coloured by species (instead of species type)
colour_pal <- c("gold", "forestgreen", "cornflowerblue", "red", "magenta")
myPal <- colorFactor(colour_pal, domain = unique(map_data$species))
m <- m %>% addCircles(data = map_data, lng = ~x, lat = ~y,
color = myPal(map_data$species), opacity = 0.9)
m
Part 2) circles coloured by species (instead of species type)
myPal <- colorFactor("Set2", domain = unique(map_data$species))
m <- m %>% addCircles(data = map_data, lng = ~x, lat = ~y,
color = myPal(map_data$species), opacity = 0.9)
m
Part 3) a colour legend
m <- m %>% addLegend(position = "topright", title = "Species", pal = myPal,
values = map_data$species, opacity = 0.9)
m
Part 4) a scale bar showing distance in kilometers
m <- m %>% addScaleBar(position = "bottomleft",
options = scaleBarOptions(maxWidth = 200, # default = 100
imperial = FALSE))
m
First, need to convert date variable to a numeric value
head(map_data$date, 5)
## [1] "2014-01-01" "2014-01-01" "2014-01-02" "2014-01-03" "2014-01-04"
is.factor(map_data$date)
## [1] FALSE
# Use 2 functions from lubridate for conversion map_data$date_decimal <- lubridate::decimal_date(lubridate::ymd(map_data$date))
date_decimal is now a numeric variable
# Use 2 functions from lubridate for conversion map_data$date_decimal <- lubridate::decimal_date(lubridate::ymd(map_data$date)) head(map_data$date_decimal)
## [1] 2014.000 2014.000 2014.003 2014.005 2014.008 2014.014
is.numeric(map_data$date_decimal)
## [1] TRUE
Provide some colours and values of date to colorNumeric().
Either provide colours (palette = c("darkgreen", "green", "gold""))) or refer to a palette (palette = "Spectral").
dateRange <- c(2014, 2015) myPal <- leaflet::colorNumeric(palette = "Spectral", domain = dateRange) # new leaflet widget m <- leaflet() %>% addProviderTiles(providers$CartoDB.Positron)
Add circles and a legend referring to myPal
m %>% addCircles(data = map_data, lng = ~x, lat = ~y,
color = myPal(map_data$date_decimal), opacity = 0.9) %>%
addLegend(position = "topright", title = "Date",
pal = myPal, values = dateRange, opacity = 0.9,
labFormat = labelFormat(big.mark = "")) # removes a comma from 2,014
Adapt the code from previous slides to produce a map with:
1) Circles coloured by population density using the viridis palette
2) and sized by population density (higher density = larger circles)
3) legend and scale bar
Previous code to adapt:
dateRange <- c(2014, 2015)
myPal <- colorNumeric(palette = "Spectral", domain = dateRange)
m <- leaflet() %>%
addProviderTiles(provider = providers$CartoDB.Positron) %>%
addCircles(data = map_data, lng = ~x, lat = ~y,
color = myPal(map_data$date_decimal), opacity = 0.9) %>%
addLegend(position = "topright", title = "Date",
pal = myPal, values = dateRange, opacity = 0.9,
labFormat = labelFormat(big.mark = ""))
m
densityRange <- c(0.1, 12000)
myPal <- colorNumeric(palette = "viridis", domain = log(densityRange))
m <- leaflet() %>%
addProviderTiles(provider = providers$CartoDB.Positron) %>%
addCircles(data = map_data, lng = ~x, lat = ~y,
color = myPal(log(map_data$density)), opacity = 0.9) %>%
addLegend(position = "topright", title = "Human<br>density<br>(log)",
pal = myPal, values = log(densityRange), opacity = 0.9,
labFormat = labelFormat(big.mark = "")) %>%
addScaleBar(position = "bottomleft")
m
myPal <- colorQuantile(palette = "viridis", domain = map_data$density)
leaflet() %>%
addProviderTiles(provider = providers$CartoDB.Positron) %>%
addCircles(data = map_data, lng = ~x, lat = ~y, radius = 10,
color = myPal(map_data$density), opacity = 0.9) %>%
addLegend(position = "topright", title = "Human<br>density",
pal = myPal, values = map_data$density, opacity = 0.9,
labFormat = labelFormat(big.mark = ""))
Load shape data and look at the structure
region_shp <- rgdal::readOGR(dsn = "data/TZ_Region_2012_density")
## OGR data source with driver: ESRI Shapefile ## Source: "/Users/wharvey/Documents/git/ShinyCourse/Day 2/slides/data/TZ_Region_2012_density", layer: "TZ_Region_2012.density" ## with 30 features ## It has 4 fields
head(region_shp)
## An object of class "SpatialPolygonsDataFrame" ## Slot "data": ## Region_Nam Loc_ID Loc_type density ## 0 Tanga Region-Tanga Region 150.13810 ## 1 Tabora Region-Tabora Region 94.02598 ## 2 Kusini Pemba Region-Kusini Pemba Region 770.20632 ## 3 Mara Region-Mara Region 1002.31128 ## 4 Manyara Region-Manyara Region 388.34348 ## 5 Kusini Unguja Region-Kusini Unguja Region 259.94865 ## ## Slot "polygons": ## [[1]] ## An object of class "Polygons" ## Slot "Polygons": ## [[1]] ## An object of class "Polygon" ## Slot "labpt": ## [1] 38.276477 -5.217057 ## ## Slot "area": ## [1] 2.275229 ## ## Slot "hole": ## [1] FALSE ## ## Slot "ringDir": ## [1] 1 ## ## Slot "coords": ## [,1] [,2] ## [1,] 38.79584 -5.962273 ## [2,] 38.79085 -5.966766 ## [3,] 38.75925 -5.953226 ## [4,] 38.73037 -5.953226 ## [5,] 38.70474 -5.945994 ## [6,] 38.69493 -5.961519 ## [7,] 38.68901 -5.961097 ## [8,] 38.66993 -5.951635 ## [9,] 38.65506 -5.954343 ## [10,] 38.64301 -5.966209 ## [11,] 38.64212 -5.975246 ## [12,] 38.62467 -5.986490 ## [13,] 38.60746 -5.980221 ## [14,] 38.59627 -5.981297 ## [15,] 38.59628 -5.987921 ## [16,] 38.59004 -5.995619 ## [17,] 38.57907 -5.999053 ## [18,] 38.56173 -6.015714 ## [19,] 38.55362 -6.012847 ## [20,] 38.55719 -6.000735 ## [21,] 38.54945 -6.001811 ## [22,] 38.54144 -5.997303 ## [23,] 38.53499 -6.003628 ## [24,] 38.51675 -6.007845 ## [25,] 38.48736 -5.999173 ## [26,] 38.47908 -6.001138 ## [27,] 38.47756 -6.008812 ## [28,] 38.47123 -6.010938 ## [29,] 38.46991 -6.017940 ## [30,] 38.46140 -6.018723 ## [31,] 38.44807 -6.008133 ## [32,] 38.43041 -6.014513 ## [33,] 38.41987 -6.007337 ## [34,] 38.41584 -5.994451 ## [35,] 38.40819 -5.982511 ## [36,] 38.39636 -5.980656 ## [37,] 38.39404 -5.989119 ## [38,] 38.36541 -5.983091 ## [39,] 38.34073 -5.986568 ## [40,] 38.34339 -5.974281 ## [41,] 38.33168 -5.965007 ## [42,] 38.33528 -5.951791 ## [43,] 38.32369 -5.944836 ## [44,] 38.31754 -5.934055 ## [45,] 38.30387 -5.935794 ## [46,] 38.29807 -5.926752 ## [47,] 38.28746 -5.930551 ## [48,] 38.28565 -5.925426 ## [49,] 38.27025 -5.930124 ## [50,] 38.25810 -5.926469 ## [51,] 38.24504 -5.928375 ## [52,] 38.24184 -5.923734 ## [53,] 38.22567 -5.914767 ## [54,] 38.22427 -5.903577 ## [55,] 38.21781 -5.900502 ## [56,] 38.20644 -5.889740 ## [57,] 38.20490 -5.879593 ## [58,] 38.19967 -5.874366 ## [59,] 38.17938 -5.872828 ## [60,] 38.17323 -5.862066 ## [61,] 38.15257 -5.854597 ## [62,] 38.14104 -5.853828 ## [63,] 38.12823 -5.860490 ## [64,] 38.11542 -5.861259 ## [65,] 38.10697 -5.854853 ## [66,] 38.10005 -5.861002 ## [67,] 38.08109 -5.854341 ## [68,] 38.07315 -5.847679 ## [69,] 38.05752 -5.863308 ## [70,] 38.03036 -5.858953 ## [71,] 38.02293 -5.863308 ## [72,] 38.01474 -5.858953 ## [73,] 38.00679 -5.860234 ## [74,] 38.00500 -5.868689 ## [75,] 37.99783 -5.872789 ## [76,] 37.98963 -5.858696 ## [77,] 37.97041 -5.848191 ## [78,] 37.96017 -5.851010 ## [79,] 37.94736 -5.848960 ## [80,] 37.94428 -5.843066 ## [81,] 37.92609 -5.842810 ## [82,] 37.91713 -5.848703 ## [83,] 37.90829 -5.864205 ## [84,] 37.89906 -5.872063 ## [85,] 37.88882 -5.871721 ## [86,] 37.87993 -5.876162 ## [87,] 37.86525 -5.891877 ## [88,] 37.84987 -5.888461 ## [89,] 37.83723 -5.888119 ## [90,] 37.81913 -5.884020 ## [91,] 37.79975 -5.891914 ## [92,] 37.79292 -5.890657 ## [93,] 37.78794 -5.895956 ## [94,] 37.77668 -5.893480 ## [95,] 37.77028 -5.886653 ## [96,] 37.75443 -5.888554 ## [97,] 37.75522 -5.877906 ## [98,] 37.75233 -5.872865 ## [99,] 37.73559 -5.872905 ## [100,] 37.72884 -5.875601 ## [101,] 37.71656 -5.869370 ## [102,] 37.71015 -5.876324 ## [103,] 37.70549 -5.890269 ## [104,] 37.69847 -5.895385 ## [105,] 37.68880 -5.913271 ## [106,] 37.66522 -5.934685 ## [107,] 37.64060 -5.948974 ## [108,] 37.63349 -5.949270 ## [109,] 37.63060 -5.933553 ## [110,] 37.63232 -5.913240 ## [111,] 37.62657 -5.912388 ## [112,] 37.62105 -5.903891 ## [113,] 37.61155 -5.898631 ## [114,] 37.61151 -5.870563 ## [115,] 37.60826 -5.856166 ## [116,] 37.58975 -5.850648 ## [117,] 37.57932 -5.838400 ## [118,] 37.57419 -5.836457 ## [119,] 37.56418 -5.841716 ## [120,] 37.55336 -5.821287 ## [121,] 37.54477 -5.815568 ## [122,] 37.53440 -5.818808 ## [123,] 37.52201 -5.818368 ## [124,] 37.50626 -5.821185 ## [125,] 37.50253 -5.815457 ## [126,] 37.49119 -5.815672 ## [127,] 37.48784 -5.824685 ## [128,] 37.47973 -5.820306 ## [129,] 37.47845 -5.809993 ## [130,] 37.46787 -5.808367 ## [131,] 37.46007 -5.800069 ## [132,] 37.45397 -5.803102 ## [133,] 37.44192 -5.802392 ## [134,] 37.41690 -5.828133 ## [135,] 37.40837 -5.843628 ## [136,] 37.39905 -5.853811 ## [137,] 37.39486 -5.863356 ## [138,] 37.39253 -5.881487 ## [139,] 37.39373 -5.894440 ## [140,] 37.38935 -5.902811 ## [141,] 37.39447 -5.928515 ## [142,] 37.39146 -5.941036 ## [143,] 37.37603 -5.965148 ## [144,] 37.36099 -5.975335 ## [145,] 37.34541 -5.974557 ## [146,] 37.32746 -5.981498 ## [147,] 37.30244 -5.979146 ## [148,] 37.28999 -5.989759 ## [149,] 37.27595 -5.989726 ## [150,] 37.26880 -5.994789 ## [151,] 37.24659 -5.993397 ## [152,] 37.23289 -6.000076 ## [153,] 37.19193 -5.999139 ## [154,] 37.17537 -6.000518 ## [155,] 37.15388 -5.990867 ## [156,] 37.14768 -5.990333 ## [157,] 37.12732 -5.966882 ## [158,] 37.12252 -5.959508 ## [159,] 37.09851 -5.908961 ## [160,] 37.09058 -5.894361 ## [161,] 37.07366 -5.858419 ## [162,] 37.07102 -5.862148 ## [163,] 37.02389 -5.894521 ## [164,] 37.02699 -5.886102 ## [165,] 37.01974 -5.878506 ## [166,] 37.02728 -5.872364 ## [167,] 37.03348 -5.860890 ## [168,] 37.03657 -5.847443 ## [169,] 37.04351 -5.841058 ## [170,] 37.05007 -5.827823 ## [171,] 37.06125 -5.823712 ## [172,] 37.08022 -5.797669 ## [173,] 37.08568 -5.786407 ## [174,] 37.09923 -5.777239 ## [175,] 37.10264 -5.768593 ## [176,] 37.11630 -5.771520 ## [177,] 37.12842 -5.758707 ## [178,] 37.14746 -5.741227 ## [179,] 37.16469 -5.746802 ## [180,] 37.18567 -5.746760 ## [181,] 37.20132 -5.748552 ## [182,] 37.20441 -5.751857 ## [183,] 37.20541 -5.714694 ## [184,] 37.18772 -5.714381 ## [185,] 37.16526 -5.716034 ## [186,] 37.18395 -5.683050 ## [187,] 37.20910 -5.655687 ## [188,] 37.21825 -5.649763 ## [189,] 37.22204 -5.642369 ## [190,] 37.22354 -5.627709 ## [191,] 37.23340 -5.623238 ## [192,] 37.24224 -5.625803 ## [193,] 37.24667 -5.618711 ## [194,] 37.24405 -5.613802 ## [195,] 37.25656 -5.602936 ## [196,] 37.24923 -5.599484 ## [197,] 37.25551 -5.584618 ## [198,] 37.25064 -5.578907 ## [199,] 37.23746 -5.570660 ## [200,] 37.23877 -5.561721 ## [201,] 37.24675 -5.549800 ## [202,] 37.25070 -5.536397 ## [203,] 37.26981 -5.523283 ## [204,] 37.28895 -5.500551 ## [205,] 37.33002 -5.449287 ## [206,] 37.38667 -5.261727 ## [207,] 37.38667 -5.252916 ## [208,] 37.35897 -5.216411 ## [209,] 37.38020 -5.193934 ## [210,] 37.46275 -5.095832 ## [211,] 37.48229 -5.071829 ## [212,] 37.48989 -5.059062 ## [213,] 37.58429 -5.004935 ## [214,] 37.59688 -5.004935 ## [215,] 37.62913 -5.013318 ## [216,] 37.67744 -5.037718 ## [217,] 37.68557 -5.039195 ## [218,] 37.70477 -5.028857 ## [219,] 37.73535 -5.016264 ## [220,] 37.76529 -5.009256 ## [221,] 37.76970 -5.013784 ## [222,] 37.78767 -5.022348 ## [223,] 37.79233 -5.030317 ## [224,] 37.80474 -5.020589 ## 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[239,] 32.24486 -6.202263 ## [240,] 32.23410 -6.194580 ## [241,] 32.22171 -6.195760 ## [242,] 32.20312 -6.179829 ## [243,] 32.19900 -6.169423 ## [244,] 32.20070 -6.161561 ## [245,] 32.19014 -6.156818 ## [246,] 32.18955 -6.146493 ## [247,] 32.17952 -6.144133 ## [248,] 32.18116 -6.135408 ## [249,] 32.18722 -6.125016 ## [250,] 32.17952 -6.108141 ## [251,] 32.16628 -6.103555 ## [252,] 32.17067 -6.083655 ## [253,] 32.16254 -6.080453 ## [254,] 32.16919 -6.066544 ## [255,] 32.15495 -6.054576 ## [256,] 32.14530 -6.034388 ## [257,] 32.14533 -6.026261 ## [258,] 32.13379 -6.025833 ## [259,] 32.13471 -6.018262 ## [260,] 32.12623 -5.999637 ## [261,] 32.11893 -5.996437 ## [262,] 32.12124 -5.981231 ## [263,] 32.11353 -5.976437 ## [264,] 32.11040 -5.965975 ## [265,] 32.11379 -5.959208 ## [266,] 32.09823 -5.948837 ## [267,] 32.09483 -5.941837 ## [268,] 32.09313 -5.928137 ## [269,] 32.08553 -5.922337 ## [270,] 32.08493 -5.900037 ## [271,] 32.08273 -5.894437 ## [272,] 32.08883 -5.868337 ## [273,] 32.08463 -5.851937 ## [274,] 32.07613 -5.838137 ## [275,] 32.06273 -5.828237 ## [276,] 32.05323 -5.830837 ## [277,] 32.04393 -5.822637 ## [278,] 32.04125 -5.810678 ## [279,] 32.02790 -5.791330 ## [280,] 32.03231 -5.783857 ## [281,] 32.02879 -5.767283 ## [282,] 32.02506 -5.762591 ## [283,] 32.00821 -5.763499 ## [284,] 32.00308 -5.756461 ## [285,] 31.99559 -5.758322 ## [286,] 31.97829 -5.754543 ## [287,] 31.96849 -5.743279 ## [288,] 31.96005 -5.751698 ## [289,] 31.93823 -5.748261 ## [290,] 31.91928 -5.749279 ## [291,] 31.91115 -5.737139 ## [292,] 31.89983 -5.742653 ## [293,] 31.88746 -5.739466 ## [294,] 31.88485 -5.730235 ## [295,] 31.87248 -5.733374 ## [296,] 31.85933 -5.729394 ## [297,] 31.83592 -5.728557 ## [298,] 31.82648 -5.712459 ## [299,] 31.80516 -5.715842 ## [300,] 31.79382 -5.725043 ## [301,] 31.78699 -5.721866 ## [302,] 31.77698 -5.726589 ## [303,] 31.77538 -5.738710 ## [304,] 31.76746 -5.750553 ## [305,] 31.74139 -5.761830 ## [306,] 31.73350 -5.759704 ## [307,] 31.73347 -5.769983 ## [308,] 31.71951 -5.779176 ## [309,] 31.71396 -5.788652 ## [310,] 31.70951 -5.780735 ## [311,] 31.69817 -5.788089 ## [312,] 31.70210 -5.796005 ## [313,] 31.69497 -5.807849 ## [314,] 31.68786 -5.812576 ## [315,] 31.67812 -5.812553 ## [316,] 31.66994 -5.823077 ## [317,] 31.66124 -5.827273 ## [318,] 31.64993 -5.824874 ## [319,] 31.64389 -5.820643 ## [320,] 31.63521 -5.820622 ## [321,] 31.62438 -5.837199 ## [322,] 31.61649 -5.836916 ## [323,] 31.61125 -5.825834 ## [324,] 31.59336 -5.822891 ## [325,] 31.59229 -5.831849 ## [326,] 31.58386 -5.833936 ## [327,] 31.57861 -5.830233 ## [328,] 31.57443 -5.818363 ## [329,] 31.56759 -5.816237 ## [330,] 31.56446 -5.808586 ## [331,] 31.55734 -5.811994 ## [332,] 31.55210 -5.805129 ## [333,] 31.54182 -5.811164 ## [334,] 31.52946 -5.810605 ## [335,] 31.51942 -5.824283 ## [336,] 31.49286 -5.818151 ## [337,] 31.48679 -5.826304 ## [338,] 31.47864 -5.824438 ## [339,] 31.46890 -5.826783 ## [340,] 31.46390 -5.823607 ## [341,] 31.44495 -5.826454 ## [342,] 31.42917 -5.825092 ## [343,] 31.41785 -5.826378 ## [344,] 31.40893 -5.818975 ## [345,] 31.40316 -5.810525 ## [346,] 31.38557 -5.799407 ## [347,] 31.38006 -5.792803 ## [348,] 31.37322 -5.791466 ## [349,] 31.35926 -5.796960 ## [350,] 31.34638 -5.795078 ## [351,] 31.32877 -5.789492 ## [352,] 31.31931 -5.783930 ## [353,] 31.30932 -5.782583 ## [354,] 31.29637 -5.801781 ## [355,] 31.27717 -5.803976 ## [356,] 31.26956 -5.793531 ## [357,] 31.25984 -5.789812 ## [358,] 31.25302 -5.783730 ## [359,] 31.25173 -5.773976 ## [360,] 31.24471 -5.748131 ## [361,] 31.23946 -5.743899 ## [362,] 31.23233 -5.753099 ## [363,] 31.21530 -5.753856 ## [364,] 31.20265 -5.738251 ## [365,] 31.19160 -5.740587 ## [366,] 31.18695 -5.747930 ## [367,] 31.17923 -5.752014 ## [368,] 31.16890 -5.762122 ## [369,] 31.15633 -5.761783 ## [370,] 31.14572 -5.766465 ## [371,] 31.14417 -5.759778 ## [372,] 31.15799 -5.743279 ## [373,] 31.15771 -5.724933 ## [374,] 31.15433 -5.712274 ## [375,] 31.14180 -5.703566 ## [376,] 31.14282 -5.691975 ## [377,] 31.15756 -5.683135 ## [378,] 31.15681 -5.678291 ## [379,] 31.14366 -5.674880 ## [380,] 31.13798 -5.670342 ## [381,] 31.14243 -5.650315 ## [382,] 31.13877 -5.644770 ## [383,] 31.12027 -5.639487 ## [384,] 31.11475 -5.633997 ## [385,] 31.10599 -5.616207 ## [386,] 31.08892 -5.608510 ## [387,] 31.06357 -5.592492 ## [388,] 31.04586 -5.574422 ## [389,] 31.04418 -5.564982 ## [390,] 31.03802 -5.553169 ## [391,] 31.05061 -5.536052 ## [392,] 31.06631 -5.525175 ## [393,] 31.07054 -5.518865 ## [394,] 31.07005 -5.508588 ## [395,] 31.06614 -5.496719 ## [396,] 31.07801 -5.485954 ## [397,] 31.08171 -5.479379 ## [398,] 31.10305 -5.465745 ## [399,] 31.13066 -5.462934 ## [400,] 31.14724 -5.457979 ## [401,] 31.15989 -5.449322 ## [402,] 31.16752 -5.446974 ## [403,] 31.18413 -5.432531 ## [404,] 31.18628 -5.417518 ## [405,] 31.18240 -5.395636 ## [406,] 31.18692 -5.377995 ## [407,] 31.18186 -5.278944 ## [408,] 31.18018 -5.254392 ## [409,] 31.18676 -5.250986 ## [410,] 31.19964 -5.252604 ## [411,] 31.20593 -5.256575 ## [412,] 31.21277 -5.254487 ## [413,] 31.21542 -5.247379 ## [414,] 31.22543 -5.240557 ## [415,] 31.23250 -5.240885 ## [416,] 31.25126 -5.249116 ## [417,] 31.26186 -5.260297 ## [418,] 31.26727 -5.271216 ## [419,] 31.26427 -5.284094 ## [420,] 31.26770 -5.295256 ## [421,] 31.28844 -5.303244 ## [422,] 31.30055 -5.304516 ## [423,] 31.32794 -5.322434 ## [424,] 31.33930 -5.325191 ## [425,] 31.35567 -5.321143 ## [426,] 31.37038 -5.331916 ## [427,] 31.37459 -5.317151 ## [428,] 31.37086 -5.306128 ## [429,] 31.38102 -5.304761 ## [430,] 31.38225 -5.313825 ## [431,] 31.39979 -5.305088 ## [432,] 31.41992 -5.319220 ## [433,] 31.42702 -5.315893 ## [434,] 31.42565 -5.309476 ## [435,] 31.41616 -5.299938 ## [436,] 31.40509 -5.292745 ## [437,] 31.38963 -5.262298 ## [438,] 31.38414 -5.254614 ## [439,] 31.37663 -5.252441 ## [440,] 31.35570 -5.252117 ## [441,] 31.35412 -5.239330 ## [442,] 31.34209 -5.235854 ## [443,] 31.32632 -5.244423 ## [444,] 31.30940 -5.249303 ## [445,] 31.30160 -5.257489 ## [446,] 31.29821 -5.267437 ## [447,] 31.30127 -5.278344 ## [448,] 31.29091 -5.288273 ## [449,] 31.28141 -5.277886 ## [450,] 31.27995 -5.269943 ## [451,] 31.28989 -5.266607 ## [452,] 31.29208 -5.253023 ## [453,] 31.27395 -5.255530 ## [454,] 31.25599 -5.246734 ## [455,] 31.25159 -5.239052 ## [456,] 31.25308 -5.226906 ## [457,] 31.24145 -5.218034 ## [458,] 31.23312 -5.220029 ## [459,] 31.20832 -5.212289 ## [460,] 31.20281 -5.198232 ## [461,] 31.20287 -5.190612 ## [462,] 31.20987 -5.182693 ## [463,] 31.22023 -5.175726 ## [464,] 31.21826 -5.159171 ## [465,] 31.20473 -5.150387 ## [466,] 31.20407 -5.146483 ## [467,] 31.21043 -5.128337 ## [468,] 31.21048 -5.109097 ## [469,] 31.22153 -5.094327 ## [470,] 31.22450 -5.085321 ## [471,] 31.23636 -5.065844 ## [472,] 31.24685 -5.055646 ## [473,] 31.24893 -5.031298 ## [474,] 31.25836 -5.019214 ## [475,] 31.25866 -5.006297 ## [476,] 31.24909 -4.997371 ## [477,] 31.23938 -4.994568 ## [478,] 31.23367 -4.957030 ## [479,] 31.23464 -4.948660 ## [480,] 31.24422 -4.935051 ## [481,] 31.25592 -4.928624 ## [482,] 31.27596 -4.922935 ## [483,] 31.30125 -4.920608 ## [484,] 31.31008 -4.915846 ## [485,] 31.30892 -4.906514 ## [486,] 31.31228 -4.896715 ## [487,] 31.32161 -4.883103 ## [488,] 31.33715 -4.869028 ## [489,] 31.34338 -4.855887 ## [490,] 31.35843 -4.843963 ## [491,] 31.36372 -4.826752 ## [492,] 31.37757 -4.816020 ## [493,] 31.37855 -4.806932 ## [494,] 31.38830 -4.808818 ## [495,] 31.39748 -4.806226 ## [496,] 31.39407 -4.792312 ## [497,] 31.39462 -4.781125 ## [498,] 31.40132 -4.766294 ## [499,] 31.39309 -4.766275 ## [500,] 31.39354 -4.750802 ## [501,] 31.39192 -4.732710 ## [502,] 31.38756 -4.723812 ## [503,] 31.40186 -4.713076 ## [504,] 31.40825 -4.698871 ## [505,] 31.42367 -4.698488 ## [506,] 31.42918 -4.704774 ## [507,] 31.44107 -4.700723 ## [508,] 31.45693 -4.690929 ## [509,] 31.45762 -4.684050 ## [510,] 31.46627 -4.681664 ## [511,] 31.47016 -4.666198 ## [512,] 31.47621 -4.661924 ## [513,] 31.49255 -4.622540 ## [514,] 31.48374 -4.603073 ## [515,] 31.48990 -4.593152 ## [516,] 31.49075 -4.586358 ## [517,] 31.48149 -4.582783 ## [518,] 31.47549 -4.559244 ## [519,] 31.47937 -4.550051 ## [520,] 31.47302 -4.544391 ## [521,] 31.47264 -4.530484 ## [522,] 31.46619 -4.526915 ## [523,] 31.45799 -4.512887 ## [524,] 31.45888 -4.504050 ## [525,] 31.46525 -4.500235 ## [526,] 31.46272 -4.491618 ## [527,] 31.46688 -4.478868 ## [528,] 31.46594 -4.472486 ## [529,] 31.45547 -4.465447 ## [530,] 31.45744 -4.457449 ## [531,] 31.45779 -4.457219 ## [532,] 31.46123 -4.459762 ## [533,] 31.46946 -4.458777 ## [534,] 31.48412 -4.438393 ## [535,] 31.49558 -4.429166 ## [536,] 31.49560 -4.420235 ## [537,] 31.49943 -4.411311 ## [538,] 31.50611 -4.411006 ## [539,] 31.54930 -4.424170 ## [540,] 31.56836 -4.425483 ## [541,] 31.59187 -4.429675 ## [542,] 31.60300 -4.424273 ## [543,] 31.61381 -4.424294 ## [544,] 31.62303 -4.421121 ## [545,] 31.64470 -4.387666 ## [546,] 31.65297 -4.380663 ## [547,] 31.65873 -4.359938 ## [548,] 31.66478 -4.351335 ## [549,] 31.67214 -4.322319 ## [550,] 31.66676 -4.311144 ## [551,] 31.65788 -4.300282 ## [552,] 31.65570 -4.277629 ## [553,] 31.67000 -4.275102 ## [554,] 31.67925 -4.255021 ## [555,] 31.66942 -4.242244 ## [556,] 31.67038 -4.237779 ## [557,] 31.68280 -4.222807 ## [558,] 31.67682 -4.186111 ## [559,] 31.66922 -4.175890 ## [560,] 31.66669 -4.165358 ## [561,] 31.66830 -4.153558 ## [562,] 31.64322 -4.145859 ## [563,] 31.63466 -4.134679 ## [564,] 31.63594 -4.128301 ## [565,] 31.64771 -4.115561 ## [566,] 31.64869 -4.100251 ## [567,] 31.65857 -4.084636 ## [568,] 31.66017 -4.072836 ## [569,] 31.67384 -4.067435 ## [570,] 31.68295 -4.053116 ## [571,] 31.68983 -4.056091 ## [572,] 31.70997 -4.060077 ## [573,] 31.72148 -4.067276 ## [574,] 31.74298 -4.073052 ## [575,] 31.75175 -4.077695 ## [576,] 31.76976 -4.081997 ## [577,] 31.78448 -4.087916 ## [578,] 31.82776 -4.089025 ## [579,] 31.85367 -4.095190 ## [580,] 31.86650 -4.096765 ## [581,] 31.88598 -4.101780 ## [582,] 31.89869 -4.110031 ## [583,] 31.93919 -4.124360 ## [584,] 31.95196 -4.133813 ## [585,] 31.96768 -4.153484 ## [586,] 31.98409 -4.166046 ## [587,] 31.99530 -4.181288 ## [588,] 32.00242 -4.187438 ## [589,] 32.01022 -4.186312 ## [590,] 32.01381 -4.191357 ## [591,] 32.02979 -4.199801 ## [592,] 32.04031 -4.211191 ## [593,] 32.05586 -4.213302 ## [594,] 32.06404 -4.222934 ## [595,] 32.07029 -4.224894 ## [596,] 32.08111 -4.235923 ## [597,] 32.08597 -4.236347 ## [598,] 32.11093 -4.246674 ## [599,] 32.11781 -4.244621 ## [600,] 32.14580 -4.244145 ## [601,] 32.17505 -4.252152 ## [602,] 32.18513 -4.259719 ## [603,] 32.21213 -4.262153 ## [604,] 32.22274 -4.260301 ## [605,] 32.23195 -4.267092 ## [606,] 32.24229 -4.265432 ## [607,] 32.25180 -4.270051 ## [608,] 32.26991 -4.270464 ## [609,] 32.28827 -4.275176 ## [610,] 32.30809 -4.267857 ## [611,] 32.32544 -4.269077 ## [612,] 32.33115 -4.273288 ## [613,] 32.34572 -4.278244 ## [614,] 32.35655 -4.287150 ## [615,] 32.35634 -4.294070 ## [616,] 32.36854 -4.305944 ## [617,] 32.38358 -4.309161 ## [618,] 32.40150 -4.323837 ## [619,] 32.41231 -4.304063 ## [620,] 32.41865 -4.283209 ## [621,] 32.41970 -4.251114 ## [622,] 32.41029 -4.227108 ## [623,] 32.40700 -4.211103 ## [624,] 32.42253 -4.210162 ## [625,] 32.43965 -4.213246 ## [626,] 32.44356 -4.211293 ## [627,] 32.46398 -4.221237 ## [628,] 32.48447 -4.227589 ## [629,] 32.49701 -4.221948 ## [630,] 32.50216 -4.214845 ## [631,] 32.50224 -4.192010 ## [632,] 32.50713 -4.185544 ## [633,] 32.52187 -4.178086 ## [634,] 32.53163 -4.176310 ## [635,] 32.53767 -4.179151 ## [636,] 32.54779 -4.193003 ## [637,] 32.56378 -4.200461 ## [638,] 32.58011 -4.201349 ## [639,] 32.58473 -4.217331 ## [640,] 32.58864 -4.243257 ## [641,] 32.59219 -4.251426 ## [642,] 32.59008 -4.285925 ## [643,] 32.61183 -4.277917 ## [644,] 32.63107 -4.273116 ## [645,] 32.64324 -4.272664 ## [646,] 32.65184 -4.268392 ## [647,] 32.66406 -4.266120 ## [648,] 32.67116 -4.259930 ## [649,] 32.68571 -4.254922 ## [650,] 32.69668 -4.253491 ## [651,] 32.70801 -4.248663 ## [652,] 32.72225 -4.246499 ## [653,] 32.74096 -4.236586 ## [654,] 32.74501 -4.227929 ## [655,] 32.73556 -4.207748 ## [656,] 32.73007 -4.186465 ## [657,] 32.69722 -4.190118 ## [658,] 32.68149 -4.173847 ## [659,] 32.67358 -4.167888 ## [660,] 32.66091 -4.166778 ## [661,] 32.64744 -4.146012 ## [662,] 32.63846 -4.129737 ## [663,] 32.65923 -4.126369 ## [664,] 32.67270 -4.118512 ## [665,] 32.67775 -4.097185 ## [666,] 32.69122 -4.086522 ## [667,] 32.69290 -4.071368 ## [668,] 32.68785 -4.041623 ## [669,] 32.70087 -4.000413 ## [670,] 32.70179 -3.986926 ## [671,] 32.70002 -3.967858 ## [672,] 32.70343 -3.945012 ## [673,] 32.74224 -3.945987 ## [674,] 32.75265 -3.951062 ## [675,] 32.77976 -3.950604 ## [676,] 32.79204 -3.952702 ## [677,] 32.81243 -3.950147 ## [678,] 32.82367 -3.940186 ## [679,] 32.83491 -3.935489 ## [680,] 32.84336 -3.920586 ## [681,] 32.84905 -3.915942 ## [682,] 32.85718 -3.915917 ## [683,] 32.89425 -3.921270 ## [684,] 32.90625 -3.924687 ## [685,] 32.92157 -3.925727 ## [686,] 32.92386 -3.919326 ## [687,] 32.93332 -3.914209 ## [688,] 32.95100 -3.912928 ## [689,] 32.97996 -3.907111 ## [690,] 33.01270 -3.906215 ## [691,] 33.02199 -3.915435 ## [692,] 33.02786 -3.937255 ## [693,] 33.03858 -3.941378 ## [694,] 33.04309 -3.946418 ## [695,] 33.06321 -3.956267 ## [696,] 33.06829 -3.962738 ## [697,] 33.08699 -3.966058 ## [698,] 33.10153 -3.965312 ## [699,] 33.12018 -3.961988 ## [700,] 33.13432 -3.957633 ## [701,] 33.14213 -3.961583 ## [702,] 33.15085 -3.959291 ## [703,] 33.15650 -3.962325 ## [704,] 33.17936 -3.959400 ## [705,] 33.18723 -3.956649 ## [706,] 33.19350 -3.949317 ## [707,] 33.20118 -3.950637 ## [708,] 33.20727 -3.956816 ## [709,] 33.21846 -3.955145 ## [710,] 33.21958 -3.944303 ## [711,] 33.22423 -3.933567 ## [712,] 33.22996 -3.931449 ## [713,] 33.24454 -3.934069 ## [714,] 33.26787 -3.916117 ## [715,] 33.28110 -3.915097 ## [716,] 33.30824 -3.905099 ## [717,] 33.31489 -3.908821 ## [718,] 33.32972 -3.899673 ## [719,] 33.34592 -3.899805 ## [720,] 33.35403 -3.893132 ## [721,] 33.35968 -3.897238 ## [722,] 33.37066 -3.890565 ## [723,] 33.38154 -3.890360 ## [724,] 33.38678 -3.893645 ## [725,] 33.39694 -3.886870 ## [726,] 33.40557 -3.889744 ## [727,] 33.41285 -3.886972 ## [728,] 33.41963 -3.897444 ## [729,] 33.43647 -3.904322 ## [730,] 33.43852 -3.909661 ## [731,] 33.45176 -3.909179 ## [732,] 33.46142 -3.900814 ## [733,] 33.49480 -3.908140 ## [734,] 33.50348 -3.904884 ## [735,] 33.51813 -3.905698 ## [736,] 33.52600 -3.896744 ## [737,] 33.53784 -3.893245 ## [738,] 33.54214 -3.896117 ## [739,] 33.55619 -3.889965 ## [740,] 33.56021 -3.882905 ## [741,] 33.57766 -3.885348 ## [742,] 33.58234 -3.880465 ## [743,] 33.60012 -3.876684 ## [744,] 33.60845 -3.882080 ## [745,] 33.61903 -3.883640 ## [746,] 33.62146 -3.879979 ## [747,] 33.63672 -3.883801 ## [748,] 33.65352 -3.892444 ## [749,] 33.65843 -3.902847 ## [750,] 33.64887 -3.920160 ## [751,] 33.65589 -3.927437 ## [752,] 33.67903 -3.937537 ## [753,] 33.71522 -3.939978 ## [754,] 33.72414 -3.943415 ## [755,] 33.73580 -3.940189 ## [756,] 33.75501 -3.927481 ## [757,] 33.76595 -3.935708 ## [758,] 33.78600 -3.938268 ## [759,] 33.79736 -3.951486 ## [760,] 33.80837 -3.947897 ## [761,] 33.81749 -3.951716 ## [762,] 33.83057 -3.951952 ## [763,] 33.83861 -3.955854 ## 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[475,] 37.05007 -5.827823 ## [476,] 37.04351 -5.841058 ## [477,] 37.03657 -5.847443 ## [478,] 37.03348 -5.860890 ## [479,] 37.02728 -5.872364 ## [480,] 37.01974 -5.878506 ## [481,] 37.02699 -5.886102 ## [482,] 37.02389 -5.894521 ## [483,] 36.99885 -5.917656 ## [484,] 36.99529 -5.913665 ## [485,] 36.96399 -5.925185 ## [486,] 36.95071 -5.924873 ## [487,] 36.92374 -5.926827 ## [488,] 36.88387 -5.945588 ## [489,] 36.85404 -5.951309 ## [490,] 36.82902 -5.939219 ## [491,] 36.78889 -5.936069 ## [492,] 36.76438 -5.937783 ## [493,] 36.75467 -5.936742 ## [494,] 36.73653 -5.938495 ## [495,] 36.71479 -5.943593 ## [496,] 36.71029 -5.922927 ## [497,] 36.69708 -5.895028 ## [498,] 36.66613 -5.848334 ## [499,] 36.64372 -5.826237 ## [500,] 36.59987 -5.797355 ## [501,] 36.59591 -5.782141 ## [502,] 36.58729 -5.768271 ## [503,] 36.57912 -5.751337 ## [504,] 36.57781 -5.743598 ## [505,] 36.53359 -5.726312 ## [506,] 36.52254 -5.700665 ## [507,] 36.51386 -5.690972 ## [508,] 36.49807 -5.686047 ## [509,] 36.49033 -5.679247 ## [510,] 36.47641 -5.676869 ## [511,] 36.47045 -5.679097 ## [512,] 36.46324 -5.671490 ## [513,] 36.44834 -5.672413 ## [514,] 36.43106 -5.667884 ## [515,] 36.44143 -5.655924 ## [516,] 36.44029 -5.636313 ## [517,] 36.43340 -5.627717 ## [518,] 36.42027 -5.621882 ## [519,] 36.41755 -5.601725 ## [520,] 36.41002 -5.599174 ## [521,] 36.39220 -5.583394 ## [522,] 36.37747 -5.573552 ## [523,] 36.34050 -5.542578 ## [524,] 36.33328 -5.538843 ## [525,] 36.30413 -5.516319 ## [526,] 36.28823 -5.496930 ## [527,] 36.26955 -5.482589 ## [528,] 36.25781 -5.462164 ## [529,] 36.24641 -5.408685 ## [530,] 36.28567 -5.412210 ## [531,] 36.29814 -5.415632 ## [532,] 36.29615 -5.362595 ## [533,] 36.29367 -5.331367 ## [534,] 36.29318 -5.300140 ## [535,] 36.27499 -5.242317 ## [536,] 36.27332 -5.230607 ## [537,] 36.27779 -5.221484 ## [538,] 36.29993 -5.205317 ## [539,] 36.26955 -5.196999 ## [540,] 36.27851 -5.179407 ## [541,] 36.28975 -5.171649 ## [542,] 36.29649 -5.157806 ## [543,] 36.31907 -5.094663 ## [544,] 36.32286 -5.078871 ## [545,] 36.31663 -5.054230 ## [546,] 36.31361 -5.025775 ## [547,] 36.31299 -5.008369 ## [548,] 36.32133 -4.990130 ## [549,] 36.32313 -4.975302 ## [550,] 36.32313 -4.955422 ## [551,] 36.32531 -4.943153 ## [552,] 36.32795 -4.912675 ## [553,] 36.33721 -4.887468 ## [554,] 36.33657 -4.845413 ## [555,] 36.32609 -4.836474 ## [556,] 36.30802 -4.812489 ## [557,] 36.30415 -4.785266 ## [558,] 36.30329 -4.746408 ## [559,] 36.30042 -4.726293 ## [560,] 36.29266 -4.697057 ## [561,] 36.29621 -4.668008 ## [562,] 36.28790 -4.622074 ## [563,] 36.28870 -4.610512 ## [564,] 36.28736 -4.587307 ## [565,] 36.29621 -4.570766 ## [566,] 36.30084 -4.544466 ## [567,] 36.30782 -4.520210 ## [568,] 36.32676 -4.499941 ## [569,] 36.32643 -4.483660 ## [570,] 36.32131 -4.476456 ## [571,] 36.33024 -4.464697 ## [572,] 36.34105 -4.440079 ## [573,] 36.34537 -4.435148 ## [574,] 36.29619 -4.422854 ## [575,] 36.24967 -4.412554 ## [576,] 36.20548 -4.407237 ## [577,] 36.17624 -4.404912 ## [578,] 36.14069 -4.399928 ## [579,] 36.10148 -4.401589 ## [580,] 36.08719 -4.398931 ## [581,] 36.04898 -4.395276 ## [582,] 36.02339 -4.396273 ## [583,] 35.99988 -4.394679 ## [584,] 35.97943 -4.380651 ## [585,] 35.95904 -4.370768 ## [586,] 35.94127 -4.365722 ## [587,] 35.90216 -4.347849 ## [588,] 35.88755 -4.343434 ## [589,] 35.86496 -4.342469 ## [590,] 35.85716 -4.337546 ## [591,] 35.84339 -4.333236 ## [592,] 35.83698 -4.324089 ## [593,] 35.81774 -4.312735 ## [594,] 35.81658 -4.336179 ## [595,] 35.81774 -4.344064 ## [596,] 35.81133 -4.360675 ## [597,] 35.81700 -4.373291 ## [598,] 35.81679 -4.388220 ## [599,] 35.79776 -4.392741 ## [600,] 35.77926 -4.399049 ## [601,] 35.77474 -4.398103 ## [602,] 35.76357 -4.404472 ## [603,] 35.74604 -4.420172 ## [604,] 35.74492 -4.432508 ## [605,] 35.72270 -4.449197 ## [606,] 35.71460 -4.451510 ## [607,] 35.69536 -4.468121 ## [608,] 35.68695 -4.472116 ## [609,] 35.68285 -4.481158 ## [610,] 35.66351 -4.486099 ## [611,] 35.65876 -4.491651 ## [612,] 35.65583 -4.506284 ## [613,] 35.65163 -4.508808 ## [614,] 35.65836 -4.539086 ## [615,] 35.65279 -4.552438 ## [616,] 35.65583 -4.562425 ## [617,] 35.66435 -4.575041 ## [618,] 35.66098 -4.588289 ## [619,] 35.65342 -4.593965 ## [620,] 35.65110 -4.608999 ## [621,] 35.64269 -4.624769 ## [622,] 35.62419 -4.641801 ## [623,] 35.61326 -4.656309 ## [624,] 35.60653 -4.671974 ## [625,] 35.60822 -4.687307 ## [626,] 35.59445 -4.700974 ## [627,] 35.57857 -4.711803 ## [628,] 35.54956 -4.729044 ## [629,] 35.53548 -4.742217 ## [630,] 35.52726 -4.762154 ## [631,] 35.51735 -4.778879 ## [632,] 35.51180 -4.792152 ## [633,] 35.50592 -4.816895 ## [634,] 35.48724 -4.839502 ## [635,] 35.47967 -4.844263 ## [636,] 35.45983 -4.847193 ## [637,] 35.41589 -4.867188 ## [638,] 35.40253 -4.859680 ## [639,] 35.37610 -4.864319 ## [640,] 35.35870 -4.856506 ## [641,] 35.35010 -4.856079 ## [642,] 35.34037 -4.876764 ## ## ## ## Slot "plotOrder": ## [1] 1 ## ## Slot "labpt": ## [1] 36.54808 -4.53372 ## ## Slot "ID": ## [1] "4" ## ## Slot "area": ## [1] 3.78614 ## ## ## [[6]] ## An object of class "Polygons" ## Slot "Polygons": ## [[1]] ## An object of class "Polygon" ## Slot "labpt": ## [1] 39.423146 -6.238686 ## ## Slot "area": ## [1] 0.07245558 ## ## Slot "hole": ## [1] FALSE ## ## Slot "ringDir": ## [1] 1 ## ## Slot "coords": ## [,1] [,2] ## [1,] 39.27878 -6.027963 ## [2,] 39.29502 -6.026602 ## [3,] 39.32966 -6.034940 ## [4,] 39.33859 -6.032004 ## [5,] 39.39572 -6.023934 ## [6,] 39.40121 -6.021609 ## [7,] 39.40990 -6.039812 ## [8,] 39.40838 -6.050178 ## [9,] 39.41437 -6.057343 ## [10,] 39.42333 -6.057808 ## [11,] 39.43129 -6.072347 ## [12,] 39.42584 -6.089948 ## [13,] 39.42870 -6.112995 ## [14,] 39.42546 -6.118239 ## [15,] 39.42545 -6.135899 ## [16,] 39.42861 -6.144457 ## [17,] 39.43494 -6.150328 ## [18,] 39.43799 -6.159055 ## [19,] 39.43801 -6.171122 ## [20,] 39.41981 -6.181386 ## [21,] 39.42342 -6.189269 ## [22,] 39.44435 -6.179159 ## [23,] 39.45054 -6.191441 ## [24,] 39.46148 -6.191527 ## [25,] 39.46516 -6.182103 ## [26,] 39.47961 -6.182016 ## [27,] 39.48099 -6.194641 ## [28,] 39.48984 -6.195429 ## [29,] 39.49487 -6.183844 ## [30,] 39.50340 -6.191671 ## [31,] 39.50664 -6.177672 ## [32,] 39.50346 -6.161963 ## [33,] 39.49922 -6.152047 ## [34,] 39.48969 -6.140820 ## [35,] 39.49637 -6.122608 ## [36,] 39.51079 -6.127606 ## [37,] 39.51917 -6.153461 ## [38,] 39.52822 -6.170188 ## [39,] 39.53477 -6.187206 ## [40,] 39.53575 -6.196637 ## [41,] 39.53338 -6.227418 ## [42,] 39.53649 -6.259255 ## [43,] 39.53694 -6.279485 ## [44,] 39.54477 -6.310405 ## [45,] 39.55723 -6.342903 ## [46,] 39.56547 -6.356002 ## [47,] 39.56948 -6.367438 ## [48,] 39.58026 -6.383563 ## [49,] 39.57528 -6.407509 ## [50,] 39.57070 -6.416749 ## [51,] 39.56822 -6.430035 ## [52,] 39.55466 -6.448346 ## [53,] 39.53053 -6.469330 ## [54,] 39.51603 -6.476294 ## [55,] 39.49562 -6.477160 ## [56,] 39.48760 -6.473494 ## [57,] 39.47371 -6.455829 ## [58,] 39.46571 -6.449421 ## [59,] 39.45634 -6.429154 ## [60,] 39.45565 -6.419205 ## [61,] 39.44184 -6.401707 ## [62,] 39.43411 -6.376402 ## [63,] 39.43319 -6.351902 ## [64,] 39.43078 -6.343436 ## [65,] 39.42136 -6.327594 ## [66,] 39.41158 -6.319457 ## [67,] 39.41494 -6.308694 ## [68,] 39.40787 -6.305172 ## [69,] 39.40435 -6.316413 ## [70,] 39.38646 -6.309847 ## [71,] 39.40099 -6.326545 ## [72,] 39.41546 -6.347157 ## [73,] 39.41606 -6.367958 ## [74,] 39.40995 -6.375005 ## [75,] 39.40301 -6.377186 ## [76,] 39.39851 -6.365993 ## [77,] 39.38734 -6.365165 ## [78,] 39.38579 -6.358258 ## [79,] 39.38918 -6.348141 ## [80,] 39.38337 -6.338810 ## [81,] 39.38306 -6.328763 ## [82,] 39.37382 -6.324133 ## [83,] 39.36123 -6.305649 ## [84,] 39.34744 -6.302858 ## [85,] 39.34127 -6.288876 ## [86,] 39.33780 -6.271705 ## [87,] 39.32724 -6.252795 ## [88,] 39.31797 -6.248465 ## [89,] 39.30996 -6.237057 ## [90,] 39.30686 -6.222955 ## [91,] 39.28778 -6.207119 ## [92,] 39.28505 -6.192836 ## [93,] 39.27457 -6.180707 ## [94,] 39.27866 -6.169825 ## [95,] 39.27063 -6.152037 ## [96,] 39.27192 -6.139334 ## [97,] 39.27000 -6.129695 ## [98,] 39.27406 -6.120969 ## [99,] 39.27811 -6.093694 ## [100,] 39.27503 -6.086431 ## [101,] 39.27642 -6.070410 ## [102,] 39.28593 -6.047105 ## [103,] 39.27878 -6.027963 ## ## ## ## Slot "plotOrder": ## [1] 1 ## ## Slot "labpt": ## [1] 39.423146 -6.238686 ## ## Slot "ID": ## [1] "5" ## ## Slot "area": ## [1] 0.07245558 ## ## ## ## Slot "plotOrder": ## [1] 2 5 1 4 6 3 ## ## Slot "bbox": ## min max ## x 31.038017 39.855694 ## y -6.976504 -1.027046 ## ## Slot "proj4string": ## CRS arguments: +proj=longlat +ellps=WGS84 +no_defs
Use addPolygons() to add to leaflet map. label = determines what will be shown when cursor hovers above area.
m <- leaflet() %>% addProviderTiles(provider = providers$Esri.WorldShadedRelief)
m %>% addPolygons(data = region_shp, label = region_shp$Region_Nam,
color = "black", weight = 1, fillOpacity = 0.3, opacity = 0.6)
Use highlightOptions() to highlight shapes when cursor hovers above. bringToFront = TRUE avoids potential problems with order in which shapes are coded in shape file.
m %>% addPolygons(data = region_shp, label = region_shp$Region_Nam, fillColor = "gold",
color = "black", weight = 1, fillOpacity = 0.3, opacity = 0.6,
highlightOptions = highlightOptions(color = "white", weight = 3,
bringToFront = TRUE, opacity = 1))
Possible to use addPolylines() to add outlines only to leaflet map.
m %>% addPolylines(data = region_shp, color = "red", weight = 2, opacity = 1)
Choropleth: Map with areas shaded according to some numeric variable
(similar to heatmap but uses geographic boundaries)
myPal <- colorNumeric(palette = "YlOrRd", domain = region_shp$density)
m %>% addPolygons(data = region_shp, label = region_shp$Region_Nam,
fillColor = myPal(region_shp$density), fillOpacity = 0.7,
color = "white", opacity = 1, weight = 2)
Like before, we can log density to give a more informative map
myPal <- colorNumeric(palette = "YlOrRd", domain = log(region_shp$density))
m %>% addPolygons(data = region_shp, label = region_shp$Region_Nam,
fillColor = myPal(log(region_shp$density)), fillOpacity = 0.7,
color = "white", opacity = 1, weight = 2)
Adjust the choropleth code below to:
colorQuantile() instead of colorNumeric()m <- leaflet() %>% addProviderTiles(provider = providers$Esri.WorldShadedRelief)
myPal <- colorNumeric(palette = "YlOrRd", domain = log(region_shp$density))
m %>% addPolygons(data = region_shp, label = region_shp$density,
fillColor = myPal(log(region_shp$density)), fillOpacity = 0.7,
color = "white", opacity = 1, weight = 2)
Subset using map_data[map_data$species == "human",] or alternatively dplyr::select()
With colorQuantile(), we don't need to log density
Create a second colour palette for data with colorNumeric().
human_data <- map_data[map_data$species == "human",]
myPal <- colorQuantile(palette = "YlOrRd", domain = region_shp$density)
myPal2 <- colorNumeric(palette = "viridis", domain = human_data$date_decimal)
m %>% addPolygons(data = region_shp, label = region_shp$density,
fillColor = myPal(region_shp$density), fillOpacity = 0.7,
color = "white", opacity = 1, weight = 2) %>%
addCircleMarkers(data = human_data, lat = ~y, lng = ~x,
fillColor = myPal2(human_data$date_decimal), fillOpacity = 0.7, radius = 4,
stroke = T, weight = 2, color = "black", opacity = 0.8)
human_data <- map_data[map_data$species == "human",]
myPal <- colorQuantile(palette = "YlOrRd", domain = region_shp$density)
myPal2 <- colorNumeric(palette = "viridis", domain = human_data$date_decimal)
m %>% addPolygons(data = region_shp, label = region_shp$density,
fillColor = myPal(region_shp$density), fillOpacity = 0.7,
color = "white", opacity = 1, weight = 2) %>%
addCircleMarkers(data = human_data, lat = ~y, lng = ~x,
fillColor = myPal2(human_data$date_decimal), fillOpacity = 0.7, radius = 4,
stroke = T, weight = 2, color = "black", opacity = 0.8)
labels <- sprintf("<strong>%s</strong><br/>%g people / km<sup>2</sup>",
region_shp$Region_Nam, round(region_shp$density, 0)) %>%
lapply(htmltools::HTML)
m %>% addPolygons(data = region_shp, fillColor = myPal(region_shp$density), label = labels,
weight = 2, opacity = 1, color = "white", fillOpacity = 0.7,
highlightOptions = highlightOptions(color = "black", weight = 3,
bringToFront = TRUE, opacity = 1))
Load data using raster() from the raster package
density <- raster::raster("../../Day 1/data/HumanPopulation.grd")
density
## class : RasterLayer ## dimensions : 259, 267, 69153 (nrow, ncol, ncell) ## resolution : 0.041665, 0.041665 (x, y) ## extent : 29.32649, 40.45105, -11.77259, -0.9813543 (xmin, xmax, ymin, ymax) ## coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 ## data source : /Users/wharvey/Documents/git/ShinyCourse/Day 1/data/HumanPopulation.grd ## names : TZA_popmap10adj_v2b ## values : 0, 29089.56 (min, max)
We can use the base plotting function plot() on the object we've created
plot(density)
Logging density will provide more texture to map
plot(log(density))
We use colorNumeric() again, as we did to colour by date earlier
colour_pal <- c("#FFFFCC", "#41B6C4", "#0C2C84")
raster::values(density) %>% range(na.rm = T)
## [1] 0.00 29089.56
myPal <- colorNumeric(palette = colour_pal, domain = c(0, 30000), na.color = "red") m <- leaflet() %>% addRasterImage(x = density, colors = myPal, opacity = 0.8)
m
Let's log density as we did before
raster::values(density) %>% range(na.rm = T) %>% log
## [1] -Inf 10.27813
myPal <- colorNumeric(palette = colour_pal, domain = c(-1.5, 11),
na.color = "transparent")
We have to exclude some data, as there are 0 density polygons and log(0) gives -infinity
sum(raster::values(density) > exp(-1.5), na.rm = T) / sum(raster::values(density) >= 0, na.rm = T)
## [1] 0.9975207
Plot the logged raster data with some tiles and a legend for the colour scheme.
m <- leaflet() %>%
addProviderTiles(provider = providers$CartoDB.Positron) %>%
addRasterImage(x = log(density), colors = myPal, opacity = 0.8) %>%
addLegend(pal = myPal, values = c(-1.5, 11), opacity = 0.8,
title = "Human<br>population<br>density")
## Warning in colors(.): Some values were outside the color scale and will be ## treated as NA
Instead of using addProviderTiles(provider = providers$CartoDB.Positron)
We order things here so that we plot
providers$CartoDB.PositronNoLabels)addRasterImage())providers$CartoDB.PositronOnlyLabels)m <- leaflet() %>%
addProviderTiles(provider = providers$CartoDB.PositronNoLabels) %>%
addRasterImage(x = log(density), colors = myPal, opacity = 0.8) %>%
addProviderTiles(provider = providers$CartoDB.PositronOnlyLabels) %>%
addLegend(pal = myPal, values = c(-1.5, 11), opacity = 0.8,
title = "Human<br>population<br>density")
Adapt the code below to add region outlines that highlight when the cursor hovers an area. Use addPolygon() with fillOpacity = 0
colour_pal <- c("#FFFFCC", "#41B6C4", "#0C2C84")
myPal <- colorNumeric(palette = colour_pal, domain = c(-1.5, 11),
na.color = "transparent")
m <- leaflet() %>%
addProviderTiles(provider = providers$CartoDB.PositronNoLabels) %>%
addRasterImage(x = log(density), colors = myPal, opacity = 0.8) %>%
addProviderTiles(provider = providers$CartoDB.PositronOnlyLabels) %>%
addLegend(pal = myPal, values = c(-1.5, 11), opacity = 0.8,
title = "Human<br>population<br>density")
## Warning in colors(.): Some values were outside the color scale and will be ## treated as NA
m <- leaflet() %>%
addProviderTiles(provider = providers$CartoDB.PositronNoLabels) %>%
addRasterImage(x = log(density), colors = myPal, opacity = 0.8) %>%
addProviderTiles(provider = providers$CartoDB.PositronOnlyLabels) %>%
addLegend(pal = myPal, values = c(-1.5, 11), opacity = 0.8,
title = "Human<br>population<br>density") %>%
addPolygons(data = region_shp, label = region_shp$Region_Nam, fillOpacity = 0,
color = "black", weight = 1, opacity = 0.6,
highlightOptions = highlightOptions(color = "white", weight = 3,
bringToFront = TRUE, opacity = 1))